Find the magnitude of the initial acceleration of a uniform sphere with mass 0.0

Question

Find the magnitude of the initial acceleration of a uniform sphere with mass 0.010 kg if released from rest at point P and acted on only by forces of gravitational attraction of the spheres at Aand B.

Exercise 13.5 Part A Two uniform spheres, each of mass 0.260 kg, are fixed at points A and B (the figure (Figure 1)). Find the magnitude of the initial acceleration of a uniform sphere with mass 0.010 kg if released from rest at point P and acted on only by forces of gravitational attraction of the spheres at A and B Express your answer using two significant figures a=12 . 10-9 m/s Submit My Answers Give Up Incorrect, One attempt remaining, Iry Again Not quite. Check through your calculations; you may have made a rounding error or used the wrong number of significant figures Figure 1 Part B Find the direction of the initial acceleration of a uniform sphere with mass 0.010 kg upward to the right downward to the left 0.010 kg Cm 10.0 cm 0.260 kg 0.260 k 6.0 cm Submit My Answers Give Up 8.0 cm | 8.0 cm Correct vide Feedback Continue

Explanation / Answer

Let

m = 0.01 kg

M = 0.26 kg

Force exerted by A and b on sphere p,

F = G*M*m/d^2

= 6.67*10^-11*0.01*0.26/0.1^2

= 1.7342*10^-11 N

angle made by this force woth vertical, theta = tan^-1(8/6)

= 53.1 degrees

net force acting on the ball placed at p,

Fnet = 2*F*cos(53.1)

= 2*1.7342*10^-11*cos(53.1)

= 2.082*10^-11 N

so, acceleration, a = Fnet/m

= 2.082*10^-11/0.01

= 2.082*10^-9

= 2.1*10^-9 m/s^2 <<<<<<<---------Answer

direction : downward

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